Break-even analysis
- Contribution margin
- CM = p − v
- Break-even quantity
- QBE = FC/(p − v)
- Target profit
- Q = (FC + profit)/(p − v)
- Profit
- π = (p − v)·Q − FC
- Margin of safety
- (Q − QBE)/Q
Management Accounting: cram pack
Formula sheets, the key method steps for every topic and 4 practice problems, with full solutions at the back.
1Formulas and methods
2Practice problems
1.Break-even analysisMedium
A product sells for €14 per unit with a variable cost of €6 per unit. Fixed costs are €8 000 per month. How many units Q must be sold per month to make a profit of €2 000?
F = €8 000p = €14v = €6profit = €2 000
Q = units
2.Break-even analysisHard
A company sells 2 250 units at €38 each, with a variable cost of €30 per unit and fixed costs of €12 000. By what percentage %ΔΠ does operating profit change if sales volume falls by 15%?
Q = 2 250p = €38v = €30F = €12 000%ΔQ = −15%
%ΔΠ = %
3.Financial accountingMedium
At 31 December, electricity used in December (€800) has not yet been billed. Which year-end entry is correct?
- ADebit electricity expense, credit accruals
- BNo entry until the bill arrives
- CDebit prepayments, credit cash
- DDebit accruals, credit electricity expense
4.Financial accountingHard
A company records routine repair costs as additions to non-current assets instead of expenses. What is the effect this year?
- AProfit is understated and assets are overstated
- BProfit and assets are overstated
- CProfit and assets are understated
- DOnly cash is affected
3Solutions
1.Break-even analysis
Answer: Q = 1250 units
Cost-volume-profit: each unit sold earns a contribution margin, price minus variable cost per unit. Profit = Q·(p − v) − F, where F is the fixed cost. At the break-even point profit is zero, so Q = F/(p − v).
Contribution margin per unit
p − v = 14 − 6 = €8
Units for the target profit
Q = (F + profit)/(p − v) = (8 000 + 2 000)/8 = 1 250
Answer
Q = 1 250 units
2.Break-even analysis
Answer: %ΔΠ = −45 %
Operating leverage: fixed costs make profit react more strongly than sales. The degree of operating leverage DOL = contribution margin/operating profit tells you that a 1% change in sales changes profit by DOL %. It is very high just above break-even and falls as sales grow.
Contribution margin and profit
CM = 2 250·8 = €18 000
Π = 18 000 − 12 000 = €6 000
DOL
DOL = 18 000/6 000 = 3
Change in profit
%ΔΠ = 3·(−15%) = −45%
Answer
%ΔΠ = −45%
Check: new profit = 1 913·8 − 12 000 = €3 300.00.
3.Financial accounting
Answer: A · Debit electricity expense, credit accruals
Why this is the answer
The accrual records December's cost as an expense this year with a current liability, so expenses match the period of use.
Answer
A · Debit electricity expense, credit accruals
4.Financial accounting
Answer: B · Profit and assets are overstated
Why this is the answer
Capitalising expenses moves cost out of profit into assets, so both are overstated now. Later depreciation spreads the cost over future years.
Answer
B · Profit and assets are overstated
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